Let Rand R' be rings and let : R R' be a ring homomorphism such

Question:

Let Rand R' be rings and let ∅ : R → R' be a ring homomorphism such that ∅[R] ≠ {0'}. Show that if R has unity 1 and R' has no 0 divisors, then ∅(1) is unity for R'.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

See More Books

Question Posted: Jan 05, 2023 05:26 AM

See More Questions

Let R be a commutative ring with unity u. a) For any (fixed) a R, prove that aR = {ar| r R] is an ideal of R. b) If the only ideals of R are {z} and R, prove that R is a field.
Let R be a ring with unity u. Prove that the units of R form a group under the multiplication of the ring.
Let R be a commutative ring with unity u, and let I be an ideal of R. (a) If u 1, prove that I = R. (b) If I contains a unit of R, prove that I = R.
Codominance observable effect on the phenotype of a heter neither allele is recessive-both alleles are dominant. 6. Which of the genotypes results in a blood type that provides clear evidence of...
Someone has two job offers and must decide which to accept. The job in City A pays $47,000 and the average cost of living there is $65,000, with a standard deviation of $15,000. The job in City B...
Sketch a reasonably simple combinational circuit implementing each of the functions from Exercise 2.6.
Electrons are made to flow through the copper strip of Figure P27.57. The strip's cross section is $1.00 \mathrm{~mm}$ high and $30.5 \mathrm{~mm}$ wide, and the strip is placed in a...
Worthmore Bank and Trust is considering giving Madsen Company a loan. Before doing so, it decides that further discussions with Madsens accountant may be desirable. One area of particular concern is...
12345678 7 9 10 Define Corporate Planning. What is Vision? What is Mission? Give an Example. What is Strategy? Define Environmental Scanning. List out elements of Internal Environment. List out...
The Internet marketing paradigm includes both marketing inputs and marketing actions. Discuss the major components of both the inputs and the actions and why it is necessary for them to work together.
Find a Grobner basis for the indicated ideal in R[x]. (x 4 - 4x 3 + 5x 2 - 2x, x 3 - x 2 - 4x + 4, x 3 - 3x + 2)
Give a one- or two-sentence synopsis of "if' part of Theorem 27.9. Data from Theorem 27.9 Let R be a commutative ring with unity. Then M is a maximal ideal of R if and only if R/M is a field. Proof...
Determine convergence or divergence using any method covered so far. n=4 1 n-9
US business culture may tend to be more corporate minded and pays more attention to face value and proper packaging. In Asia on the other hand, free products are valued and the proper service and...
What is power? How does one acquire power and what is the best kind of power to have? How do I preserve the power that I have? How do I influence someone with power and make sure that my message...
How do unionized organizations handle complaints and grievances from employees? Explain briefly
Provide your reaction to the statement: "Employee benefits are seen by employees are an entitlement for their membership in companies or organizations." Explain your response.
Describe the historical impact of early British settlement on Aboriginal and/or Torres Strait Islander peoples.
Go to the IRS Web site (www.irs.gov) and print the first page of Form 1040. Compute Pierre Lappin's adjusted gross income by entering the following information on Form 1040: $60,000 salary, $5,000...
Compare and contrast licensing and subcontracting.
The New York Stock Exchange has reported that the average number of stocks directly held by senior citizens is 4.3, compared to 2.0 stocks for Baby Boomers. Assume that data file XR11014 contains the...
Using the sample results in Exercise 11.14, construct and interpret the 90% confidence interval for the difference between the population means. Is the hypothesized difference (0.00) within the...
It has been reported that the average visitor from Japan spent $1953 during a trip to the United States, while the average for a visitor from the United Kingdom was $1783. Assuming that file XR11029...
8. In the game shown, player 1 learns his type and sends a message, and then both players 1 and 2 simultaneously choose actions. Find a separating per- fect Bayes-Nash equilibrium. 1 W 2 a Type s...
1) Do you think lobbying is a beneficial organization group for some, or is it just "legalized bribery" which should be made illegal? 2) Does privatization of certain government provided services...
What is Foreign Direct Investment (FDI): Disney, a US-based company, is investing in India, which is considered a foreign direct investment. FDI is a critical driver of economic growth for developing...

Let Rand R' be rings and let : R R' be a ring homomorphism such

Question:

Step by Step Answer:

By Theorem 263 we know 1 is unity for R Suppose that R has unity 1 Then 1 11 11 so that we have 11 1...View the full answer

A First Course In Abstract Algebra

Students also viewed these Mathematics questions